Math exam 2 concepts

What is a combination?

A combination is a group of items taken without regard to their order

Explain how to find N!, where N is a positive integer.

N! Can be found by finding the product of all positive integers from n down through 1.

How to distinguish between permutation and combination problems-

Permutation problems involve situations in which order matters and combination problems involve situations in which the order of the items makes no difference.

Advantage of Fundamental Counting Principle rather than a tree diagram

The Fundamental Counting Principle can be used to more easily find the number of possible outcomes in situations with a series of many successive things.

nPr represents

The notation nPr represents the number of permutations of n things taken r at a time.

How is the number of permutations in RARE determined?

The number of permutations can be found by dividing the factorial of letters in the word by the factorial of the number of letters that are the same in the word.

Fundamental counting principle

If you can choose one item from a group of M items and a second item for a group of N items, then the total number of two item choices is MxN

Make sense or not- "Assuming that it might rain tomorrow or that it might not rain at all, the probability of it not raining tomorrow is .5

The statement does not make sense because an event can have two outcomes with different chances of occurring.

How is the theoretical probability of an event computed?

The theoretical probability of an event can be found by dividing the number of outcomes in the event by the number of outcomes in its sample space.

Describe the difference between theoretical probability and empirical probability-

Theoretical probability applies to situation in which the sample space only contains equally likely outcomes, all of which are known. By contrast, empirical probability applies to situations in which we observe how frequently an event occurs.

Make sense or not- "I estimate there are approximately 10,000 ways to arrange the letters A,B,C,D...X,Y,Z"

This statement does not make sense because according to the Fundamental Counting Principle, the number of ways to arrange the letters is equal to 26x25x24.... 2x1 and is much greater than 10,000.

Makes sense or not- "There are more than 100 possible sets of answers on a seven item true\false test"

This statement makes sense because according to the Fundamental Counting Principle, the number of possible sets of answers on a seven item true/false test is 2^7th power and this value is more than 100.

Does this make sense or not make sense- "I used the Fundamental Counting Principle to determine the number of 5 digit zip codes that are available to the US postal service."

This statement makes sense because the Fundamental Counting Principle is used to find the number of ways in which a series of successive things can occur.

If 24 permutations can be formed using letters in the word RATE, can 24 permutations also be formed using the letters in the word RARE?

No, the word RARE cannot form as many permutations because it has a duplicate letter.

Best way to evaluate 800!/799! Without a calculator

Rewrite 800! As 800x (799!) and then cancel out 799! From the numerator and denominator.

Use the Definition of probability to explain why the probability of an event that cannot occur is 0.

The probability of an event that cannot occur is 0 because the event has no possible outcomes

Use the definition of theoretical probability to explain why the probability of an event that is certain n to occur is 1-

The probability of an event that is certain to occur is 1 because the event has the same outcomes as the sample space

Permutation or combination- "A medical researcher needs 18 people to test the effectiveness of an experimental drug. If 60 people have volunteered for the test, in how many ways can 18 people be selected?

The problem involves a combination because the order of patients selected does not matter.

Permutation or combination- "How many different 4 letter passwords can be formed from the letters H, I, J, K, L, M, and N if no repetition of letters is allowed?

The problem involves a permutation because the order of letters selected does matter.

What is the sample space of an experiment? What event?

The set of all possible outcomes of an experiment is the sample space of the experiment, denoted by S. An event, denoted by E, is any subset of a sample space.